Properties

Label 50820i
Number of curves $2$
Conductor $50820$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 50820i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50820.g1 50820i1 \([0, -1, 0, -68405, -6863250]\) \(1248870793216/42525\) \(1205370104400\) \([2]\) \(168000\) \(1.4098\) \(\Gamma_0(N)\)-optimal
50820.g2 50820i2 \([0, -1, 0, -65380, -7500920]\) \(-68150496976/14467005\) \(-6561070552270080\) \([2]\) \(336000\) \(1.7564\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50820i have rank \(0\).

Complex multiplication

The elliptic curves in class 50820i do not have complex multiplication.

Modular form 50820.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} - 4 q^{13} - q^{15} - 2 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.